Complex functions of one variable, Cauchy-Riemann equations, Cauchy theorem and integral formula, singularities, residue theorem, index of closed curves, analytic continuation, conformal mappings, Riemann mapping theorem.

Complex functions of one variable, Cauchy-Riemann equations, Cauchy theorem and integral formula, singularities, residue theorem, special functions, conformal mappings, Riemann mapping theorem.

Introduction to linear algebra: vectors and matrices, solving systems of linear equations, vector spaces and subspaces, orthogonality and least squares, determinants, eigenvalues and eigenvectors, singular value decomposition and linear transformations. Applications in and links to computer science will be presented in parallel.

Mostly self-contained, but fast-paced, introductory masters level course on various theoretical aspects of algorithms that aim to extract information from data.

Mostly self-contained, but fast-paced, introductory masters level course on various theoretical aspects of algorithms that aim to extract information from data.

Introductory course to Mathematical aspects of Signal Processing, Network Theory, and Machine Learning. It showcases how different areas of Mathematics (including, but not limited to: Linear Algebra, Probability, Number Theory, Statistics, Combinatorics) interact and find applications in Data Science and related fields.

This student seminar will focus on Statistical-to-Computational Gaps, a topic in the interface of Theoretical Computer Science, Statistics, and High Dimensional Probability.